• in situ calibration
• CDF
• top quark mass
• Matrix Element method
• Quasi Monte Carlo
• likelihood
• W+jets background
• transfer functions
• jet energy scale

The discovery of the bottom quark in 1977 at the Tevatron Collider triggered the search for its partner in the third fermion isospin doublet, the top quark, which was discovered 18 years later in 1995 by the CDF and D0 experiments during the Tevatron Run I. By 1990, intensive efforts by many groups at several accelerators had lifted to over 90 GeV the lower mass limit, such that since then the Tevatron became the only accelerator with high-enough energy to possibly discover this amazingly massive quark. After its discovery, the determination of top quark properties has been one of the main goals of the Fermilab Tevatron Collider, and more recently also of the Large Hadron Collider (LHC) at CERN. Since the mass value plays an important role in a large number of theoretical calculations on fundamental processes, improving the accuracy of its measurement has been at any time a goal of utmost importance.

Predominantly produced in ttbar pairs at the Tevatron through strong interactions in ppbar collisions, the top quark mass was measured for the first time by CDF with a value of 176 ± 13 GeV/c^2, showing that this particle was by far the heaviest known elementary particle. This has raised many questions on whether the top quark may play a special role in the Standard Model (SM), in particular in the electroweak symmetry breaking. Due to the huge mass and the very short lifetime (∼ 5 × 10−25 s), about six times shorter than the strong interaction timescale, the top quark decays weakly before hadronization into a W boson and a b quark , giving the chance to study the properties of a bare quark. Top quark pair events are thus characterized by the decay of their two final state W bosons. This leads the ttbar pairs to generate the experimental signatures of two jets associated with the hadronization of the bottom quarks and either a single lepton (e, μ, τ), one undetected neutrino and two light quark jets (lepton+jets channel), or four light quark jets (all-jets channel), or two leptons (ee, eμ, μμ, eτ, μτ, ττ) and two undetected neutrinos (dilepton channels). Up to now, because of its difficult experimental signatures the τ lepton was not exploited in the mass studies.

Different approaches have been followed by the Tevatron experiments to determine the top quark mass. A very powerful technique is the Matrix Element (ME) method which determines the likelihood of observing an event under both ttbar and background hypotheses. The hypotheses are determined from the entire kinematic information associated to every single event by integrating the matrix element of the process over the multidimensional phase space describing the final state. For a given sample of selected events, the parameters to be measured are then determined as those values that maximize the overall likelihood. The superior statistical sensitivity of this method, with respect to other methods based on distribution-fitting, is due to the completeness of the information exploited in each event.

Since the top quark mass is a fundamental parameter of the SM, the CDF Collaboration has decided to make a major effort in order to produce its most precise measurement as a "legacy" of the experiment. A number of improvements over previous measurements are still possible as mentioned below, noticeably comparing the signal candidates not only to the signal expectation, but also to the expectation of the dominant background process (W +jets), whose SM matrix element is now made available to the Collaboration. This thesis provides an overview of the preparatory studies to the final CDF measurement of the top quark mass. We investigate the lepton + jets channel with the full integrated luminosity of Run II (9.0 fb−1). Our analysis uses the ME method to calculate a ttbar likelihood as a bi-dimensional function of the assumed top mass mt and ∆JES. ∆JES parametrizes the uncertainty in our knowledge of the jet energy scale. It is a shift applied to all jet energies in units of the jet-dependent systematic error. By introducing this parameter into the likelihood, we can use as a constraint the known W mass to determine the optimal ∆JES and thereby reduce the final systematic error on the measured top quark mass. For the first time in CDF analyses, we include the background ME modeling in the likelihood integration, with an expected significant reduction of the systematic error of the final result.

The massive calculations required by this double ME method imposed to develop an unconventional, less time-consuming, integration method over the phase space of the events kinematics. In order to evaluate the multidimensional integrals, we employ the "Quasi Monte Carlo" (QMC) technique, based on deterministic sequences generated by choosing points approximately equally spaced in the integration space, such that equal phase space volumes contain approximately equal number of points. This technique significantly reduces the time required to integrate an event, allowing us to reduce greatly the integration time needed to reach the required precision. It also imposes extensive studies to make sure that no bias is introduced relative to a standard MC calculation.

The present thesis describes in detail the contributions given by the candidate to the massive preparation work needed to make the new analysis possible, during her 8 months long stay at Fermilab. These include selection of the candidates within looser cuts than in the past, estimate of the expected number of signal and background events, evaluation of the acceptance, model comparison of the final validation plots, optimization of the integration method and of its systematic error, and more as described in chapters 4 to 7.
Chapter 1 gives a brief introduction of top quark physics. Some previous mass measurements, as well as the refinements introduced in our analysis, are discussed.
Chapter 2 contains the description of the Tevatron accelerator complex and the CDF II detector.
Chapter 3 describes the reconstruction of the physical objects on which the event analysis relies.
The event selection is described in Chapter 4, where the complete list of the selection requirements and the estimation of the sample composition are presented, as well as the comparison between model and data.
Chapter 5 explains the ME method in detail, examining each part of the likelihood expression, and Chapter 6 deals with the QMC integration employed in the analysis.
In Chapter 7 the current status of the analysis and the future steps required to perform the measurement are described. Preliminarily to the final analysis of real data, future studies will include a calibration procedure and evaluation of systematic errors by means of pseudo-experiments. The goal of the measurement is to reach a total error of about 0.6 GeV/c^2, about 20% less than the present error of the world-averaged mass value. The candidate is planning to contribute from a distance to this final part of the measurement.